Answer:[tex]\ln \frac{(x+2)}{x^4(x^2+6)}[/tex]Explanations:
The given logarithmic expression is:
[tex]\frac{1}{9}\ln (x+2)^9-\frac{1}{4}\lbrack\ln (x^{16})-\ln (x^2+6)^4\rbrack[/tex]
Expand the given expression
[tex]\frac{1}{9}\ln (x+2)^9-\frac{1}{4}\ln (x^{16})-\frac{1}{4}\ln (x^2+6)^4[/tex]
It can be further simplified as:
[tex]\begin{gathered} \ln (x+2)^{\frac{9}{9}}-\ln (x^{\frac{16}{4}})-\ln (x^2+6)^{\frac{4}{4}} \\ \ln (x+2)-\ln (x^4)-\ln (x^2+6) \end{gathered}[/tex]
The expression can be written as a single logarithm as shown below:
[tex]\ln \frac{(x+2)}{x^4(x^2+6)}[/tex]
